Expected Distances on Manifolds of Partially Oriented Flags
| Autor: | Chris Peterson, Brenden Balch, Clayton Shonkwiler |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Mathematics - Differential Geometry
Pure mathematics Computer science Applied Mathematics General Mathematics Flag (linear algebra) 0211 other engineering and technologies 021107 urban & regional planning Metric Geometry (math.MG) 010103 numerical & computational mathematics 02 engineering and technology 53D30 (primary) 60D05 51N35 (secondary) 01 natural sciences Linear subspace Orientation (vector space) Mathematics - Metric Geometry Differential geometry Differential Geometry (math.DG) Homogeneous space FOS: Mathematics Generalized flag variety 0101 mathematics Algebraic number Mathematics::Representation Theory Vector space |
| DOI: | 10.48550/arxiv.2001.07854 |
| Popis: | Flag manifolds are generalizations of projective spaces and other Grassmannians: they parametrize flags, which are nested sequences of subspaces in a given vector space. These are important objects in algebraic and differential geometry, but are also increasingly being used in data science, where many types of data are properly understood as subspaces rather than vectors. In this paper we discuss partially oriented flag manifolds, which parametrize flags in which some of the subspaces may be endowed with an orientation. We compute the expected distance between random points on some low-dimensional examples, which we view as a statistical baseline against which to compare the distances between particular partially oriented flags coming from geometry or data. Comment: 13 pages, 3 figures |
| Databáze: | OpenAIRE |
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